An adjusting sleeve assembly includes an adjusting sleeve slidably mounted around an upright support member of a sunshade and a mounting member extending outward from the adjusting sleeve and including a U-shape path therein. A pivotal block is pivotally mounted in the mounting member. A connecting rod includes a first end connected to the pivotal block to pivot therewith and a second end pivotally connected to an arcuate tube for supporting a canopy of the sunshade. A push member is slidably received in the pivotal block and includes an end for manual operation. A positioning peg includes a first end securely attached to the push member to move therewith and a second end that is urged into one of two positioning ends of the U-shape path for retaining the connecting rod in place with respect to the mounting member.